High-pressure studies of a biphasic NiTiSn/Ni2TiSn Heusler alloy by in situ X-ray diffraction and first principle calculations.
Introduction
Over the last few decades, the crystallization of the NiTiSn and Ni2TiSn compounds as half-Heusler (HH) and full-Heusler (FH) alloys have gained increasing attention, mainly due to its promising thermoelectric characteristics with excellent electrical properties[1] [2], good mechanical robustness [3] and high thermal stability [4]. These materials are composed of non-expensive, abundant and non-toxic elements [5] that can be easily synthesized by green routes such as standard solid-state methods [4], [6], arc melting, rapid solidification and open die pressing [7], combination of arc-melting, ball-milling and spark plasma sintering [8], mechanical alloying [9], [10] among others.
The performance of a thermoelectric material might be improved if its thermal conductivity is reduced without a strong degradation of its electrical properties. In general, structural and chemical defects play an important role as phonon scattering centers, contributing to the reduction of thermal conductivity. For example, in a recent theoretical study, Dey and Dutta [11] were able to understand the origin of the long-standing discrepancy between ab initio prediction and experimental results on the type of conductivity in these alloys considering the interstitial defects in HF systems (NbCoSn, TiCoSb, and NiTiSn). In the same way, Dasmahapatra et al.[12], using a more realistic model and considering interstitial defects, explained the low band gap of NiTiSn and showed that the power-factor was almost twice of that of the defect-free NiTiSn.
Experimentally, the thermal conductivity has been shown to be sensitive to microstructure (crystallites sizes and microstrains), grain boundaries [13], stoichiometric variations, vacancies, occupation of crystallographic sites, doping and secondary phases [7] which in turn is directly linked to the synthesis method [5], [14], [15], [16], [17], [18], [19]. For example, a reduction between 10% and 30% in thermal conductivity with increase of 50% in the electrical conductivity was reported for a biphasic bulk alloy, composed of Ni2TiSn and NiTiSn, prepared by induction levitation melting process and this phenomenon was attributed to the NiTiSn/Ni2TiSn interfacial scattering [20]. In a similar way, the reported improvement in the electrical power factor of a nanosized half-Heusler NiTiSn alloy, produced by milling and sintering [21], was attributed to the existence of Ni2TiSn nanoprecipitates [15]. Another recent work on a biphasic Nb-Co-Sn system consisting of NbCo2Sn full Heusler precipitates embedded in a NbCoSn half Heusler matrix [13] showed that the improvement in the thermoelectric properties were related to phonon scattering in misfit defects on the HH/FH interfaces [13].
An easy way to obtain these alloys, in a nanostructured form, with high defect concentration and grain boundaries, is the mechanical alloying (MA). MA involves milling of a solid powder with high mechanical energy provided by the high frequency collisions between hard metallic spheres and the sample particles. MA is a particularly interesting solid-state reaction technique that is able to produce a large amount of metastable phases [22] like nanocrystals [23], supersaturated solid solutions [24] and amorphous alloys [25]. It is difficult to assess the exact role of high energetic collisions in the solid-state reactions mechanism as it depends on many variables [26] which occasionally invokes criticism of the efficacy of MA technique [27]. However, it has been successfully used over the years to synthesize a number of mechanically alloyed multiphase and even single phase nanostructured materials [9], [27], [28], [29], [30].
In one of our previous studies [31], we investigated the pressure dependencies of the structural and thermoelectric properties of the half-Heusler NiTiZ (Z = Si, Ge, Sn and Sb) alloys using the first-principle density functional study. It is important to note that among the above alloys, the half-Heusler NiTiSn demonstrates the highest dimensionless figure of merit. The value of bulk modulus of NiTiSn (B0 =133(9)GPa), calculated from a second-order Birch Murnaghan equation of state, was found to be in excellent agreement with other theoretically calculated values such as B0 = 147.81 GPa [32][33], B0 = 145.81GPa [34] and B0 = 152.67GPa [34]. These discrepancies between theoretical values could be understood as the consequence of different calculation methods and variables considered. However, a recent high pressure experimental study [35] has reported a considerably smaller bulk modulus (B0 =119.(4) GPa) [35] for half-Heusler NiTiSn compound, which is in good agreement with that obtained by using the density functional perturbation theory (DFPT):B0 = 114 GPa [36].
In this work we synthesized a two-phase (FH and HH) Ni-Ti-Sn alloy via mechanical alloying technique, using a vibrational high-energy mill. The synthesized sample was then subjected to high pressures up to 11.9 GPa and studied by in situ x-ray diffraction and Rietveld refinement methods. The crystalline evolution with pressure was investigated by DFT and the compressibility coefficients were obtained by the second-order Birch Murnaghan equation.
Section snippets
Experimental and theoretical procedure
High purity (99,9%) metallic Ni (Vetec), Ti (Aldrich) and Sn (Alfa Aesar) powders were sealed together under argon atmosphere inside a cylindrical steel vial along with several steel balls, with 5:1 ball-to-powder ratio. Mechanical Alloying was then performed at room temperature in a SPEX type mill. XRD measurements were performed using an Empyrean Panalytical diffractometer after 4 h of milling. The measurements were carried out in the angular range of 10° to 100° (2θ), with step sizes of
Results and discussion
Fig. 1(a) shows the XRD pattern of the milled sample after 4 h of processing. As can be seen, no precursor peaks were observed indicating a complete reaction between the elements. The milling time was based on earlier studies where the milling was performed in a planetary mill as a function of frequency and processing time [9]. They report that low frequencies (thus, low energies) are not sufficient to obtain a pure Heusler system until 5 h of milling. However, longer processing promotes the
Conclusions
In this work, a solid solution of the half-Heusler NiTiSn and full-Heusler Ni2TiSn phases was synthesized using the mechanical alloying technique. Due to the great structural similarity, it is difficult to visualize the presence of the full-Heusler phase. Rietveld refinement method played an important role in confirming the presence of this phase. Both phases were found to have nanometer-sized crystallites.
The synthesized sample was subjected to a high-pressure experiment using in situ x ray
CRediT authorship contribution statement
Aercio Filipe Franklim de F. Pereira: Data curation, Investigation, Formal analysis, Writing - original draft, Paola de Araújo Gomes, Data curation, Investigation. Camila Costa Pinto: Data curation, Investigation, Formal analysis, Writing – original draft. Querem Hapuque Felix Rebelo: Methodology, Formal analysis, Writing, Angsula Ghosh: Conceptualization, Data curation, Methodology, Formal analysis, Writing – original draft. Daniela Menegon Trichês: Conceptualization, Resources, Writing. João
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
We acknowledge the financial support from the Brazilian funding agencies CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nivel Superior) – CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) - Finance code 001, and FAPEAM (Fundação de Amparo à Pesquisa do Estado do Amazonas) (project code 062.01312/2018 and 062.01112/2019). We thank the Brazilian Synchrotron Light Laboratory - LNLS, XDS laboratory facilities (proposal ID: 20160500).
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